# Approximate dollar MTM of interest rate swaps

I'm definitely a fixed income tourist but I'm wondering if there's an easy way to back of the envelope approximate dollar PnL of an interest rate swap

For example, if I enter a \$1m fixed 5y USD swap at 3% and tomorrow the quote rises 5bps to 3.05%, assuming I know the carry X bps and rolldown Y bps, what is my dollar PnL of the position?

## 1 Answer

If only one day has elapsed, the carry and roll down effect on the p/l is insignificant. The p/l is well approximated simply by multiplying the move in the quotation by the duration of the swap, which in the case of a 5yr swap is around 4.5. So the p/l would be 4.5*0.05%*1MM = about 2250 dollars.

• Gotcha thanks! Why is the duration on a 5y around 4.5 years? Is it because the payments are semi annual? So for 10y would the duration be 9.5 years? Commented Jun 22, 2022 at 18:54
• It’s just the value of a 1bp annuity, calculated at prevailing interest rate. It would be more like 9.0 for a 10yr.
– dm63
Commented Jun 22, 2022 at 20:59
• ah thanks! do you by chance have any reference/ info on how to do the calculation? Commented Jun 22, 2022 at 22:42